1. Field of the Invention
The invention relates in general to the investigation of subsurface earth formations and in particular to methods and systems for measuring the dielectric constants of earth formations adjacent to a bore hole.
2. Description of the Prior Art
Normally earth formations having a high brine saturation will exhibit a low electrical resistivity while formations having a high oil saturation will exhibit a high electrical resistivity. Frequently shaliness of the formations causes formations having high oil saturation to have low electrical resistivities. It is therefore useful, in assessing the oil bearing potentials of earth formations, to be able to determine if the low resistivities are caused by shaliness of the formations. In U.S. Pat. No. 3,895,289 (1975), Rickey et al disclose a method to determine the effects of shaliness on electrical resistivity. The dielectric constants of earth formations are measured at frequencies below 50 KHz. The dielectric constant of a formation, measured at frequencies below 50 KHz, has been determined to be related to the portion of the electrical conductivity due to shaliness. See "Low Porosity Gas Sand Analysis using Cation Exchange and Dielectric Constant Data" by Kern et al in Trans. SPWLA XVII (June 1976). Therefore, methods capable of measuring in-situ the electrical resistivities and dielectric constants of earth formations at frequencies below 50 KHz are valuable in revealing information concerning oil potential in the earth formations.
Laboratory tests have shown that when an alternating electric current is passed through shaly materials and the capacitances are measured, the capacitances of the shaly materials decrease rather rapidly when the frequency of the current increases. For example, with a five percent by weight suspension of bentonite in a 20,000 parts per million NaCl solution the capacitances decrease from about 4,400 p farads at about 60 Hz to almost zero at 100 KHz. Most capacitance measurements on clay suspensions in brine have shown a similar relationship between capacity and frequency. The dielectric constants of shaly materials are proportional to the capacitances and thus also decrease with increasing frequency of the current. The results of such laboratory tests are explained in more detail in "Dielectric Constant of Rocks as a Petrophysical Parameter" by Hoyer et al in Trans SPWLA XVII (June 1976). Hence the dielectric constants of shaly earth formations at low frequencies, such as those below 50 KHz, may be very different from the dielectric constants of the same formations at high frequencies such as those in the megahertz range. In order that certain well logging systems be adaptable to apply the method disclosed by Rickey et al to determine the effects of shaliness on electrical resistivity, such well logging systems must be capable of measuring dielectric constants at frequencies below 50 KHz.
A number of well logging systems have been used in the prior art to measure in-situ the resistivity and dielectric constants of earth formations in a bore hole. Aiken, in U.S. Pat. No. 2,592,101 (1952), disclosed a system using an impedance bridge to perform such measurements. The impedance bridge used comprises three impedances connected in series but positioned spatially to form three sides of a square. The two unconnected ends of the three impedances are then connected to two electrodes in contact with and moving over the bore hole wall. The three impedances form three arms of the impedance bridge, and the portion of the earth formation between the two electrodes forms the remaining arm of the bridge. Two filters connected in series are connected across a diagonal of the incomplete square formed by the three impedances. The two filters have resonance frequencies at 400 Hz and 20 megahertz, respectively. Alternating current sources of 400 cycles and 20 megacycles are connected across the other diagonal of the incomplete square.
The values of the three impedances in the bridge are preferably chosen so that the bridge is nearly balanced when the impedance between the electrodes across the formation is approximately the minimum formation impedance encountered along the bore hole. As the electrodes move over formations of different impedances, a corresponding unbalance of the bridge is produced. When the 400 Hz alternating current is applied to the bridge the filter with resonance frequency of 20 megahertz has a negligible impedance and substantially all of the 400 Hz unbalance voltage will appear across the filter having a resonance frequency of 400 Hz. At a low frequency of 400 cycles the contribution of the reactance of the portion of the formation to the unbalance voltage compared to that of the resistance is small and the unbalance voltage is presumed to be principally a function of the resistance of the portion of the formation. The unbalance voltage is therefore a measure of the resistance of the portion of the earth formation. When the 20 megahertz alternating current is applied to the bridge, the impedance of the filter having a resonance frequency of 400 Hz is negligable and the unbalance voltage will appear across the filter having a resonance frequency of 20 megahertz. At 20 megahertz the impedance of many formations will be predominantly reactive and the unbalance voltage is assumed to be caused primarily by the reactance of the portion of the formation. The dielectric constant of the portion of the formation may be derived from the unbalance voltage.
Aiken states in the patent specification that for some formations the impedance at 20 megacycles may not be predominantly reactive. Thus for some formations, Aiken's method described above cannot be used to measure the reactance of the formations. To determine the dielectric constants of the earth formations, measurements of both the resistances and reactances of such formations are usually necessary. To measure the resistance and reactance of earth formations at locations along the bore hole the impedance bridge method requires measurements at two different frequencies instead of at only one frequency. More operations time is therefore required. For a substantial range of frequencies between 400 Hz and 20 MHz, particularly those below 50 KHz, the resistive response of the earth formation compared to the reactive response is not negligible and cannot be ignored. Aiken's system for measuring the dielectric constant functions only when the resistive response is negligible. Hence for a substantial range of frequencies below 50 KHz, Aiken's system cannot be used to determine dielectric constants of earth formations.
In the same patent to Aiken, a modified apparatus was disclosed to measure the phase difference between the current and voltage across the formation as an indication of the dielectric constant of the formation. An alternating current source of high frequency such as 20 megahertz is passed through a portion of the formation in series with a resistor. The voltage across the resistor is in phase with the current through the portion of the formation. The voltage across the resistor is supplied to an automatic volume control amplifier which provides an output voltage which is substantially constant in magnitude independent of the voltage input to the amplifier, and the phase of which bears a fixed relation to the phase of the voltage input. The voltage across the formation is also supplied to an automatic volume control amplifier to provide a constant magnitude voltage which bears a fixed phase relation to the phase of the voltage input. The two amplifiers are adjusted to provide output voltages of equal magnitude, but which are 180.degree. out of phase when there is no phase difference between the two input voltages to the two amplifiers. The output voltages of the two amplifiers are applied respectively to two resistors connected in series. Hence, if there is no phase difference between the current and voltage across the formation, the voltage across the two resistors will be equal but 180.degree. out of phase. The voltage across the two resistors is therefore zero. Typically the voltage and current across the formation are not in phase so that the voltage across the two resistors would not be zero, in which case the magnitude of this voltage is a measure of the phase difference between the current and voltage across the formation. This phase difference is known to be a function of the dielectric constant across the portion of the formation.
The automatic volume control amplifier in Aiken's phase detecting apparatus employs a variable gain and feedback device to maintain an output voltage of constant magnitude independent of variations in the input voltage to the amplifier. When the input voltage changes the gain is varied to maintain an output voltage of constant magnitude. When the gain of an amplifier is varied, however, the phase difference between the input and output voltages of the amplifier may also vary. This variable phase difference will be combined with the phase difference between the current and voltage across the formation that is to be determined. The errors may be substantial. It is quite common for the resistivity of an earth formation at one location to be many times that of an adjacent formation along the bore hole. To maintain a constant voltage output at both formations, the amplifier gain must change by a large factor, which may introduce a large phase difference appearing as noise in the phase difference measurements. It may be difficult, therefore, to accurately measure small phase differences between the voltage and the current in the formation using this method.
Aiken discloses still another modified embodiment where a high frequency current source is also used, to pass an alternating current through a portion of a formation in series with a resistor. As discussed earlier the phase difference between the voltage across the resistor and the voltage across the formation portion is the same as the phase difference between current through and voltage across the portion. A voltage bearing a definite phase relation to the voltage across the resistor is applied to the plate of a pentode. The voltage across the formation is applied to an automatic volume control amplifier to provide an output voltage of constant magnitude in phase with the input voltage to the amplifier. This output voltage is applied to the grid of the pentode through a phase adjustor and a variable voltage source. When the voltage across the resistor is in phase with the voltage across the formation portion, the phase adjustor and the variable voltage source are adjusted so that the grid voltage is just sufficient to prevent the flow of plate current. When the two voltages compared are out of phase, plate current will flow through the pentode. The larger the phase difference between the two voltages compared, the larger will be the plate current. The rectified component of this plate current is therefore a measure of the phase difference between the current through and voltage across the formation portion.
The resistance of earth formations may change typically by a large factor from location to location. The gain of the automatic volume control amplifier must change by a similar factor to maintain a constant voltage output. As discussed earlier, this variation in gain may introduce a sizable phase difference added to the phase difference between the two voltage compared, which can appear as a significant error in the measurement. Hence this embodiment cannot be used to accurately measure small phase differences between the current through and voltage across an earth formation or a portion thereof.
Aiken proposes still further systems for measuring the dielectric constants and resistivities of earth formations. Such systems employ the same phase detecting devices as those that have been described, wherein the various drawbacks described above have not been alleviated. Such systems will have the same disadvantages as those discussed earlier.
Cox et al in U.S. Pat. No. 4,012,689 (1977) discloses an induction well logging system for determining the resistivity and dielectric constant of earth materials in the vicinity of a well bore hole. A radio frequency electromagnetic field is generated in a bore hole to induce a secondary electromagnetic field and the total electromagnetic field along longitudinally spaced locations is detected. Measurements of the relative phase shift in the electromagnetic field between the detector locations and the amplitude of the field at one of the detector locations may then be interpreted according to predetermined relationships in terms of the earth formation resistivity and dielectric constant.
Instead of measuring voltages across different circuit components and the phase difference between the voltage and current through the formation, the system proposed by Cox et al measures the amplitude of the electromagnetic wave at one detector location and the relative phase shift in the wave between the detector locations. This system operates only at radio frequencies in the range from 10-60 MHz; it does not operate at lower frequencies. Thus this system cannot be used to measure the dielectric constants of earth formations at frequencies lower than such radio frequencies.
Other examples of induction well logging systems are disclosed in U.S. Pat. No. 3,891,916 (1975) to Meador et al, and in U.S. Pat. No. 3,893,021 (1975) to Meador et al.
U.S. Pat. No. 4,130,793 [1978] issued to Bridges discloses a digital apparatus for measuring the phase shift in an induction logging system as that disclosed by Cox et al discussed above. The electromagnetic field in the formation is detected at two different locations to give two different detector signals. The two signals are amplified and converted into square waves of the same frequencies by means of zero crossing detectors. The converted signals are fed into an exclusive OR gate and the width of the output signal is measured with the aid of an AND gate and a clock in terms of number of clock pulses. The number of clock pulses corresponds to the phase difference between the two detector signals and is a measure of the dielectric constant of the earth formation. This digital apparatus proposed by Bridges cannot, however, detect whether one detector signal is leading or lagging the other detector signal.